The invention relates generally to analog-to-digital (A/D) converters. More specifically, the invention relates to a fully optical A/D converter.
Many inputs provided to digital data processing systems are derived from signals that are typically analog in nature. The first step in processing an analog signal in a digital data processing system is, of course, to perform an A/D conversion. It is well known for a bandwidth limited signal with a sharp cutoff upper limit frequency of (f), an A/D converter must sample the signal at a rate of at least (4 f). For high frequency signals, such as in microwave communications and radar, the necessary sampling rates (bandwidths) cannot be achieved using electronic techniques.
Recently, electro-optic devices with gegahertz (GHz) sampling rates have been proposed and demonstrated. For example, U.S. Pat. No. 4,502,037 discloses an electro-optic A/D converter that employs a two-armed interferometer, in which the intensity of the emergent radiation is a function of a phase shift introduced by the application of a potential difference, representing the signal to be digitized, between electrodes positioned in the vicinity of at least one arm of the interferometer.
The basic theory of operation of such electro-optic A/D devices is described in detail by Becker and Leonberger in a paper entitled, "Performance Criteria of Components Required for Electrooptic Analog-to-Digital Conversion", Proceedings of SPIE, Vol. 408, Integrated Optics III, pp. 50-56 (1983), incorporated herein by reference. This paper discusses an electro-optic A/D in which high speed sampling is derived from the use of a pulsed laser source. For example, laser diodes can be used to obtain pulses of a few tens of picoseconds with GHz repetition rates. As shown in FIG. 1, the light from the pulsed laser source is introduced into an integrated optics device which consists of a multiplicity of Mach-Zehnder modulators. The electrodes of the modulators are driven electronically in parallel by the signal to be digitized. The output intensity, I.sub.o, of the modulator in response to the drive voltage, V, is given by EQU I.sub.o =I.sub.i cos.sup.2 (2.pi. .alpha. VL) (1)
where I.sub.i is the input intensity, L is the length of the electrodes and .alpha. is the electro-optic coupling coefficient with a typical value of 0.1 (V-cm).sup.-1. As shown in FIG. 1 the output intensity, I.sub.o, is detected and compared to a reference channel so as to turn on the digital output when I.sub.o is equal to 1/2 I.sub.i. Through the use of suitable bias voltages and differing electrode lengths it is possible to arrange the thresholds to occur in a pattern that produces a gray code output, a variation on binary encoding.
A fundamental difficulty with the above-described electro-optic A/D devices is that higher frequency operation can only be achieved at the expense of digitizing resolution. At high frequencies, the voltage applied to the electrodes of the modulator does not travel down the electrodes at the same velocity as the light pulse travelling through the waveguide. Typically, the light will travel twice as fast, causing the light pulse to smear out (average over) the input signal which in turn produces an error in digitalization of the signal. For a particular input frequency, f, the worse case error (sampling at the peak or trough) is given approximately by ##EQU1## where c is the speed of light, n is the index of refraction of the material, V.sub.e is the speed of the electrical signal down the electrodes and L is the electrode length. This error implies a maximum bit resolution, B.sub.r, given by ##EQU2## Note that the above analysis is for a single frequency signal, but the analysis for real bandwidth limited signals is quite similar.
If the length of the electrodes could be arbitrarily shortened, the "walk-off" phenomena described above would not be a problem. Unfortunately, the resolution of the device is also limited by the number of cycles of the cosine function in Equation 1 for the lowest order bit channel. A typical device can at best withstand about 100 volts without breaking down. Using 100 volts as the maximum voltage, V.sub.m, it can be shown that the drive voltage bit resolution is given by EQU B.sub.v = 1.44 ln (2.alpha.V.sub.m L)=1.44 ln (20L) (4)
A plot of Equations 3 and 4 is shown in FIG. 2. The intersection of the two curves gives the maximum bit resolution at a particular frequency. As can be seen, bit resolution is extremely limited for frequencies higher than about 3 GHz.